365874
Three rods each of length \(L\) and mass \(M\) are placed along \(X\). \(Y\) and \(Z\) axes in such a way that one end of each of the rod is at the origin. The moment of inertia of this system about \(Z\) axis is
1 \(\dfrac{2 M L^{2}}{3}\)
2 \(\dfrac{4 M L^{2}}{3}\)
3 \(\dfrac{5 M L^{2}}{3}\)
4 \(\dfrac{M L^{2}}{3}\)
Explanation:
\(I=\dfrac{M L^{2}}{3}+\dfrac{M L^{2}}{3}=\dfrac{2 M L^{2}}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365875
The radius of gyration of a uniform rod of length \(L\) about an axis passing through its centre of mass and perpendicular to its length is
1 \(\dfrac{\mathrm{L}}{\sqrt{2}}\)
2 \(\dfrac{\mathrm{L}^{2}}{\sqrt{12}}\)
3 \(\dfrac{L}{\sqrt{3}}\)
4 \(\dfrac{\mathrm{L}}{\sqrt{12}}\)
Explanation:
The radius of gyration \(K\) is given by \(K=\sqrt{\dfrac{I}{M}}=\sqrt{\dfrac{M L^{2} / 12}{M}}=\dfrac{L}{\sqrt{12}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365876
A sphere of mass \(10\;kg\) and radius \(0.5\;\,m\) rotates about a tangent. The moment of inertia of the solid sphere is
365877
The moment of inertia of a rigid body about an axis
1 depends on the position of axis of rotation.
2 does not depend on its size.
3 does not depend on its mass.
4 does not depend on its shape.
Explanation:
Moment of inertia of a body depends on position and orientation of axis of rotation. It also depends on shape, size of the body and also on the distribution of mass. Correct option is (1).
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PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365874
Three rods each of length \(L\) and mass \(M\) are placed along \(X\). \(Y\) and \(Z\) axes in such a way that one end of each of the rod is at the origin. The moment of inertia of this system about \(Z\) axis is
1 \(\dfrac{2 M L^{2}}{3}\)
2 \(\dfrac{4 M L^{2}}{3}\)
3 \(\dfrac{5 M L^{2}}{3}\)
4 \(\dfrac{M L^{2}}{3}\)
Explanation:
\(I=\dfrac{M L^{2}}{3}+\dfrac{M L^{2}}{3}=\dfrac{2 M L^{2}}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365875
The radius of gyration of a uniform rod of length \(L\) about an axis passing through its centre of mass and perpendicular to its length is
1 \(\dfrac{\mathrm{L}}{\sqrt{2}}\)
2 \(\dfrac{\mathrm{L}^{2}}{\sqrt{12}}\)
3 \(\dfrac{L}{\sqrt{3}}\)
4 \(\dfrac{\mathrm{L}}{\sqrt{12}}\)
Explanation:
The radius of gyration \(K\) is given by \(K=\sqrt{\dfrac{I}{M}}=\sqrt{\dfrac{M L^{2} / 12}{M}}=\dfrac{L}{\sqrt{12}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365876
A sphere of mass \(10\;kg\) and radius \(0.5\;\,m\) rotates about a tangent. The moment of inertia of the solid sphere is
365877
The moment of inertia of a rigid body about an axis
1 depends on the position of axis of rotation.
2 does not depend on its size.
3 does not depend on its mass.
4 does not depend on its shape.
Explanation:
Moment of inertia of a body depends on position and orientation of axis of rotation. It also depends on shape, size of the body and also on the distribution of mass. Correct option is (1).
365874
Three rods each of length \(L\) and mass \(M\) are placed along \(X\). \(Y\) and \(Z\) axes in such a way that one end of each of the rod is at the origin. The moment of inertia of this system about \(Z\) axis is
1 \(\dfrac{2 M L^{2}}{3}\)
2 \(\dfrac{4 M L^{2}}{3}\)
3 \(\dfrac{5 M L^{2}}{3}\)
4 \(\dfrac{M L^{2}}{3}\)
Explanation:
\(I=\dfrac{M L^{2}}{3}+\dfrac{M L^{2}}{3}=\dfrac{2 M L^{2}}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365875
The radius of gyration of a uniform rod of length \(L\) about an axis passing through its centre of mass and perpendicular to its length is
1 \(\dfrac{\mathrm{L}}{\sqrt{2}}\)
2 \(\dfrac{\mathrm{L}^{2}}{\sqrt{12}}\)
3 \(\dfrac{L}{\sqrt{3}}\)
4 \(\dfrac{\mathrm{L}}{\sqrt{12}}\)
Explanation:
The radius of gyration \(K\) is given by \(K=\sqrt{\dfrac{I}{M}}=\sqrt{\dfrac{M L^{2} / 12}{M}}=\dfrac{L}{\sqrt{12}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365876
A sphere of mass \(10\;kg\) and radius \(0.5\;\,m\) rotates about a tangent. The moment of inertia of the solid sphere is
365877
The moment of inertia of a rigid body about an axis
1 depends on the position of axis of rotation.
2 does not depend on its size.
3 does not depend on its mass.
4 does not depend on its shape.
Explanation:
Moment of inertia of a body depends on position and orientation of axis of rotation. It also depends on shape, size of the body and also on the distribution of mass. Correct option is (1).
365874
Three rods each of length \(L\) and mass \(M\) are placed along \(X\). \(Y\) and \(Z\) axes in such a way that one end of each of the rod is at the origin. The moment of inertia of this system about \(Z\) axis is
1 \(\dfrac{2 M L^{2}}{3}\)
2 \(\dfrac{4 M L^{2}}{3}\)
3 \(\dfrac{5 M L^{2}}{3}\)
4 \(\dfrac{M L^{2}}{3}\)
Explanation:
\(I=\dfrac{M L^{2}}{3}+\dfrac{M L^{2}}{3}=\dfrac{2 M L^{2}}{3}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365875
The radius of gyration of a uniform rod of length \(L\) about an axis passing through its centre of mass and perpendicular to its length is
1 \(\dfrac{\mathrm{L}}{\sqrt{2}}\)
2 \(\dfrac{\mathrm{L}^{2}}{\sqrt{12}}\)
3 \(\dfrac{L}{\sqrt{3}}\)
4 \(\dfrac{\mathrm{L}}{\sqrt{12}}\)
Explanation:
The radius of gyration \(K\) is given by \(K=\sqrt{\dfrac{I}{M}}=\sqrt{\dfrac{M L^{2} / 12}{M}}=\dfrac{L}{\sqrt{12}}\)
PHXI07:SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
365876
A sphere of mass \(10\;kg\) and radius \(0.5\;\,m\) rotates about a tangent. The moment of inertia of the solid sphere is
365877
The moment of inertia of a rigid body about an axis
1 depends on the position of axis of rotation.
2 does not depend on its size.
3 does not depend on its mass.
4 does not depend on its shape.
Explanation:
Moment of inertia of a body depends on position and orientation of axis of rotation. It also depends on shape, size of the body and also on the distribution of mass. Correct option is (1).